TeXShopInstalling TeX Live
If you downloaded MacTeX as recommended under the "Obtaining" tab, double click MacTeX to begin the installation process. Follow the same procedure if instead you obtained BasicTeX.
Some History
Users interacting with TeX using a front end program are sometimes unaware of the vast support machinery acting invisibly behind the scene. This machinery consists of Donald Knuth's command line program, which does the actual typesetting, and of an enormous number of fonts, macro packages like LaTeX and ConTeXt, style files, documentation, configuration files, and the like. The enormous collection of programs and support files is called a TeX Distribution.
For a number of years, the standard TeX distribution on Mac OS X and GNU/Linux was teTeX, maintained by Thomas Esser. On the Macintosh, this distribution was enhanced by Gerben Wierda, who wrote a program called i-Installer to download his enhanced version from the network, to configure it, and to upgrade it periodically.
Several years ago the TeX Users Group introduced an even more extensive distribution called TeX Live, for Mac OS X, Windows, GNU/Linux, and various BSD Unix systems; the principal authors are Sebastian Rahtz, Karl Berry, and Staszek Wawrykiewicz. In May, 2006, Thomas Esser announced that he would no longer support teTeX, and suggested that users move to TeX Live. Shortly afterward, Gerben Wierda stopped updating his system. Today, TeX Live (which MacTeX installs) is the standard TeX distribution on the Macintosh.
Multiple Distribution Support
When a new version of TeX Live is installed by MacTeX, the new version does not overwrite the previous version. This makes it possible for users in the middle of an important project to safely update, because they can switch back to the earlier version if they run into trouble. Switching back requires only a single button click due to a feature explained below.
Gerben Wierda and Jerome Laurens designed a data structure to support multiple TeX distributions on a machine. This data structure is installed by the MacTeX packages. The data structure is placed in /Library/TeX and consists of some carefully designed symbolic links to installed distributions. Using this structure, TeX Live and Basic TeX easily coexist on a machine.
The program "TeX Live Utility", installed in /Applications/TeX by MacTeX, contains a menu item called "Configure" which has an item called "Change Default TeX Live Version." This item opens a small dialog window listing all TeX Distributions available on a user's machine, with an indication of the active distribution. Using the dialog, a different distribution can be made active. When that happens, all GUI applications are reconfigured automatically, and PATH and MAN variables are reset for command line interaction with the new active distribution.
The data structure is ingenious; it does not modify TeX distributions in any way. Switching distributions actually modifies only a single symbolic link deep within the data structure. The data structure also contains a visible link called /Library/TeX/texbin, which points indirectly to the binary directory of the active TeX distribution. GUI applications need to be reconfigured for the data structure by using the /Library/TeX/texbin link to find the TeX binaries, but after they are configured once, they will work without modification in the future. TeXShop, BibDesk, LaTeXiT, and TeX Live Utility all use /Library/TeX/texbin automatically.